%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU147+2 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:50:43 AM UTC 2026 % Result : Theorem 15.84s 16.12s % Output : Proof 15.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU147+2 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n018.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:32:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.26/0.52 %----Proving TF0_NAR, FOF, or CNF % 15.84/16.12 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.84/16.12 --- Run --no-e-matching --full-saturate-quant at 6... % 15.84/16.12 % SZS status Theorem % 15.84/16.12 % SZS output start Proof % 15.84/16.12 ( % 15.84/16.12 (declare-sort $$unsorted 0) % 15.84/16.12 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 15.84/16.12 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.84/16.12 (declare-const tptp.empty_set $$unsorted) % 15.84/16.12 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.proper_subset (-> $$unsorted $$unsorted Bool)) % 15.84/16.12 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 15.84/16.12 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 15.84/16.12 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.84/16.12 (define @t1 () (@var "A" $$unsorted)) % 15.84/16.12 (define @t2 () (@var "B" $$unsorted)) % 15.84/16.12 (define @t3 () (not (tptp.in @t2 @t1))) % 15.84/16.12 (define @t4 () (tptp.in @t1 @t2)) % 15.84/16.12 (define @t5 () (@list @t1 @t2)) % 15.84/16.12 (define @t6 () (tptp.proper_subset @t2 @t1)) % 15.84/16.12 (define @t7 () (tptp.proper_subset @t1 @t2)) % 15.84/16.12 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 15.84/16.12 (define @t9 () (tptp.set_union2 @t2 @t1)) % 15.84/16.12 (define @t10 () (tptp.set_union2 @t1 @t2)) % 15.84/16.12 (define @t11 () (tptp.set_intersection2 @t1 @t2)) % 15.84/16.12 (define @t12 () (tptp.subset @t1 @t2)) % 15.84/16.12 (define @t13 () (= @t1 @t2)) % 15.84/16.12 (define @t14 () (forall @t5 (= @t13 (and @t12 (tptp.subset @t2 @t1))))) % 15.84/16.12 (define @t15 () (@var "C" $$unsorted)) % 15.84/16.12 (define @t16 () (tptp.in @t15 @t2)) % 15.84/16.12 (define @t17 () (= @t16 (= @t15 @t1))) % 15.84/16.12 (define @t18 () (@list @t15)) % 15.84/16.12 (define @t19 () (forall @t18 @t17)) % 15.84/16.12 (define @t20 () (tptp.singleton @t1)) % 15.84/16.12 (define @t21 () (= @t2 @t20)) % 15.84/16.12 (define @t22 () (= @t21 @t19)) % 15.84/16.12 (define @t23 () (forall @t5 @t22)) % 15.84/16.12 (define @t24 () (= @t1 tptp.empty_set)) % 15.84/16.12 (define @t25 () (@list @t1)) % 15.84/16.12 (define @t26 () (forall @t5 (= (= @t2 (tptp.powerset @t1)) (forall @t18 (= @t16 (tptp.subset @t15 @t1)))))) % 15.84/16.12 (define @t27 () (@var "D" $$unsorted)) % 15.84/16.12 (define @t28 () (tptp.in @t27 @t15)) % 15.84/16.12 (define @t29 () (@list @t27)) % 15.84/16.12 (define @t30 () (@list @t1 @t2 @t15)) % 15.84/16.12 (define @t31 () (tptp.in @t27 @t2)) % 15.84/16.12 (define @t32 () (tptp.in @t27 @t1)) % 15.84/16.12 (define @t33 () (tptp.in @t15 @t1)) % 15.84/16.12 (define @t34 () (forall @t29 (= @t28 (and @t32 @t31)))) % 15.84/16.12 (define @t35 () (= (= @t15 @t11) @t34)) % 15.84/16.12 (define @t36 () (forall @t30 @t35)) % 15.84/16.12 (define @t37 () (tptp.set_difference @t1 @t2)) % 15.84/16.12 (define @t38 () (tptp.disjoint @t1 @t2)) % 15.84/16.12 (define @t39 () (forall @t5 (= @t38 (= @t11 tptp.empty_set)))) % 15.84/16.12 (define @t40 () (not @t13)) % 15.84/16.12 (define @t41 () (tptp.empty @t1)) % 15.84/16.12 (define @t42 () (not @t41)) % 15.84/16.12 (define @t43 () (forall @t25 (not (= @t20 tptp.empty_set)))) % 15.84/16.12 (define @t44 () (tptp.singleton @t2)) % 15.84/16.12 (define @t45 () (tptp.set_intersection2 @t2 @t15)) % 15.84/16.12 (define @t46 () (tptp.subset @t1 @t15)) % 15.84/16.12 (define @t47 () (tptp.singleton tptp.empty_set)) % 15.84/16.12 (define @t48 () (tptp.powerset tptp.empty_set)) % 15.84/16.12 (define @t49 () (= @t48 @t47)) % 15.84/16.12 (define @t50 () (forall @t18 (= @t33 @t16))) % 15.84/16.12 (define @t51 () (=> @t50 @t13)) % 15.84/16.12 (define @t52 () (forall @t5 @t51)) % 15.84/16.12 (define @t53 () (tptp.set_union2 @t1 (tptp.set_difference @t2 @t1))) % 15.84/16.12 (define @t54 () (and @t33 @t16)) % 15.84/16.12 (define @t55 () (exists @t18 @t54)) % 15.84/16.12 (define @t56 () (and @t55 @t38)) % 15.84/16.12 (define @t57 () (not @t56)) % 15.84/16.12 (define @t58 () (forall @t18 (not @t54))) % 15.84/16.12 (define @t59 () (not @t38)) % 15.84/16.12 (define @t60 () (and @t59 @t58)) % 15.84/16.12 (define @t61 () (not @t60)) % 15.84/16.12 (define @t62 () (and @t61 @t57)) % 15.84/16.12 (define @t63 () (forall @t5 @t62)) % 15.84/16.12 (define @t64 () (tptp.subset @t1 tptp.empty_set)) % 15.84/16.12 (define @t65 () (forall @t25 (=> @t64 @t24))) % 15.84/16.12 (define @t66 () (tptp.in @t15 @t11)) % 15.84/16.12 (define @t67 () (tptp.empty @t2)) % 15.84/16.12 (define @t68 () (tptp.subset tptp.empty_set tptp.empty_set)) % 15.84/16.12 (define @t69 () (and @t68 @t68)) % 15.84/16.12 (define @t70 () (= (= tptp.empty_set tptp.empty_set) @t69)) % 15.84/16.12 (define @t71 () (@list tptp.empty_set tptp.empty_set)) % 15.84/16.12 (define @t72 () (@list false)) % 15.84/16.12 (define @t73 () (tptp.in @t15 @t47)) % 15.84/16.12 (define @t74 () (tptp.subset @t15 tptp.empty_set)) % 15.84/16.12 (define @t75 () (forall @t18 (= @t73 @t74))) % 15.84/16.12 (define @t76 () (= (= @t47 @t48) @t75)) % 15.84/16.12 (define @t77 () (@list tptp.empty_set @t47)) % 15.84/16.12 (define @t78 () (forall @t18 (= @t74 @t73))) % 15.84/16.12 (define @t79 () (= @t49 @t78)) % 15.84/16.12 (define @t80 () (not @t78)) % 15.84/16.12 (define @t81 () (@list true false)) % 15.84/16.12 (define @t82 () (@quantifiers_skolemize @t78 0)) % 15.84/16.12 (define @t83 () (tptp.in @t82 @t47)) % 15.84/16.12 (define @t84 () (tptp.subset @t82 tptp.empty_set)) % 15.84/16.12 (define @t85 () (= @t84 @t83)) % 15.84/16.12 (define @t86 () (not @t84)) % 15.84/16.12 (define @t87 () (= @t82 tptp.empty_set)) % 15.84/16.12 (define @t88 () (or @t86 @t87)) % 15.84/16.12 (define @t89 () (forall @t25 (or (not @t64) @t24))) % 15.84/16.12 (define @t90 () (@list @t82)) % 15.84/16.12 (define @t91 () (= tptp.empty_set @t82)) % 15.84/16.12 (define @t92 () (or @t86 @t91)) % 15.84/16.12 (define @t93 () (forall @t18 (= @t16 @t33))) % 15.84/16.12 (define @t94 () (= tptp.empty_set @t47)) % 15.84/16.12 (define @t95 () (tptp.in @t15 tptp.empty_set)) % 15.84/16.12 (define @t96 () (forall @t18 (= @t73 @t95))) % 15.84/16.12 (define @t97 () (not @t96)) % 15.84/16.12 (define @t98 () (or @t97 @t94)) % 15.84/16.12 (define @t99 () (forall @t5 (or (not @t93) @t13))) % 15.84/16.12 (define @t100 () (forall @t18 (= @t95 @t73))) % 15.84/16.12 (define @t101 () (not @t100)) % 15.84/16.12 (define @t102 () (or @t101 @t94)) % 15.84/16.12 (define @t103 () (not (= @t47 tptp.empty_set))) % 15.84/16.12 (define @t104 () (@var "BOUND_VARIABLE_7854" $$unsorted)) % 15.84/16.12 (define @t105 () (@var "BOUND_VARIABLE_7868" $$unsorted)) % 15.84/16.12 (define @t106 () (not (tptp.in @t105 @t104))) % 15.84/16.12 (define @t107 () (@var "BOUND_VARIABLE_7852" $$unsorted)) % 15.84/16.12 (define @t108 () (not (tptp.in @t105 @t107))) % 15.84/16.12 (define @t109 () (not (tptp.disjoint @t107 @t104))) % 15.84/16.12 (define @t110 () (or @t108 @t106)) % 15.84/16.12 (define @t111 () (or @t110 @t109)) % 15.84/16.12 (define @t112 () (forall (@list @t107 @t104 @t105) @t111)) % 15.84/16.12 (define @t113 () (@list @t105)) % 15.84/16.12 (define @t114 () (forall @t113 @t111)) % 15.84/16.12 (define @t115 () (@list @t107 @t104)) % 15.84/16.12 (define @t116 () (forall @t113 @t110)) % 15.84/16.12 (define @t117 () (or @t116 @t109)) % 15.84/16.12 (define @t118 () (forall @t115 (or (forall @t18 (or (not (tptp.in @t15 @t107)) (not (tptp.in @t15 @t104)))) @t109))) % 15.84/16.12 (define @t119 () (@var "BOUND_VARIABLE_7839" $$unsorted)) % 15.84/16.12 (define @t120 () (@var "BOUND_VARIABLE_7837" $$unsorted)) % 15.84/16.12 (define @t121 () (forall (@list @t120 @t119) (or (tptp.disjoint @t120 @t119) (not (forall @t18 (or (not (tptp.in @t15 @t120)) (not (tptp.in @t15 @t119)))))))) % 15.84/16.12 (define @t122 () (forall @t18 (or (not @t33) (not @t16)))) % 15.84/16.12 (define @t123 () (or @t122 @t59)) % 15.84/16.12 (define @t124 () (forall @t5 @t123)) % 15.84/16.12 (define @t125 () (@list @t1 @t2)) % 15.84/16.12 (define @t126 () (not @t122)) % 15.84/16.12 (define @t127 () (or @t38 @t126)) % 15.84/16.12 (define @t128 () (forall @t5 @t127)) % 15.84/16.12 (define @t129 () (and @t128 @t124)) % 15.84/16.12 (define @t130 () (and (not (and @t59 @t122)) (not (and @t126 @t38)))) % 15.84/16.12 (define @t131 () (not @t58)) % 15.84/16.12 (define @t132 () (@quantifiers_skolemize @t100 0)) % 15.84/16.12 (define @t133 () (tptp.disjoint tptp.empty_set tptp.empty_set)) % 15.84/16.12 (define @t134 () (tptp.set_intersection2 tptp.empty_set tptp.empty_set)) % 15.84/16.12 (define @t135 () (= @t134 tptp.empty_set)) % 15.84/16.12 (define @t136 () (= @t133 @t135)) % 15.84/16.12 (define @t137 () (= tptp.empty_set @t134)) % 15.84/16.12 (define @t138 () (= @t137 @t133)) % 15.84/16.12 (define @t139 () (= @t11 @t15)) % 15.84/16.12 (define @t140 () (tptp.in @t27 tptp.empty_set)) % 15.84/16.12 (define @t141 () (and @t140 @t140)) % 15.84/16.12 (define @t142 () (= @t140 @t141)) % 15.84/16.12 (define @t143 () (forall @t29 @t142)) % 15.84/16.12 (define @t144 () (= @t143 @t135)) % 15.84/16.12 (define @t145 () (forall @t30 (= @t34 @t139))) % 15.84/16.12 (define @t146 () (@list false false)) % 15.84/16.12 (define @t147 () (tptp.in @t132 tptp.empty_set)) % 15.84/16.12 (define @t148 () (not @t147)) % 15.84/16.12 (define @t149 () (not @t133)) % 15.84/16.12 (define @t150 () (or @t149 @t148 @t148)) % 15.84/16.12 (define @t151 () (tptp.in @t132 @t47)) % 15.84/16.12 (define @t152 () (= @t147 @t151)) % 15.84/16.12 (define @t153 () (@list true true)) % 15.84/16.12 (define @t154 () (forall @t18 (= (= @t15 tptp.empty_set) @t73))) % 15.84/16.12 (define @t155 () (= tptp.empty_set @t15)) % 15.84/16.12 (define @t156 () (forall @t18 (= @t73 @t155))) % 15.84/16.12 (define @t157 () (= (= @t47 @t47) @t156)) % 15.84/16.12 (define @t158 () (forall @t5 (= @t21 (forall @t18 (= @t16 (= @t1 @t15)))))) % 15.84/16.12 (define @t159 () (= @t132 tptp.empty_set)) % 15.84/16.12 (define @t160 () (= @t159 @t151)) % 15.84/16.12 (define @t161 () (= tptp.empty_set @t132)) % 15.84/16.12 (define @t162 () (= @t151 @t161)) % 15.84/16.12 (define @t163 () (@list @t154)) % 15.84/16.12 (define @t164 () (not @t151)) % 15.84/16.12 (define @t165 () (not @t91)) % 15.84/16.12 (define @t166 () (not @t161)) % 15.84/16.12 (define @t167 () (not @t83)) % 15.84/16.12 (define @t168 () (= false true)) % 15.84/16.12 (define @t169 () (and @t151 @t161 @t91 @t167)) % 15.84/16.12 (define @t170 () (= @t87 @t83)) % 15.84/16.12 (define @t171 () (= @t83 @t91)) % 15.84/16.12 (define @t172 () (not @t68)) % 15.84/16.12 (define @t173 () (and @t68 @t91 @t86)) % 15.84/16.12 (assume @p1 (forall @t5 (=> @t4 @t3))) % 15.84/16.12 (assume @p2 (forall @t5 (=> @t7 (not @t6)))) % 15.84/16.12 (assume @p3 (forall @t5 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 15.84/16.12 (assume @p4 (forall @t5 (= @t10 @t9))) % 15.84/16.12 (assume @p5 (forall @t5 (= @t11 (tptp.set_intersection2 @t2 @t1)))) % 15.84/16.12 (assume @p6 @t14) % 15.84/16.12 (assume @p7 @t23) % 15.84/16.12 (assume @p8 (forall @t25 (= @t24 (forall (@list @t2) @t3)))) % 15.84/16.12 (assume @p9 @t26) % 15.84/16.12 (assume @p10 (forall @t30 (= (= @t15 @t8) (forall @t29 (= @t28 (or (= @t27 @t1) (= @t27 @t2))))))) % 15.84/16.12 (assume @p11 (forall @t30 (= (= @t15 @t10) (forall @t29 (= @t28 (or @t32 @t31)))))) % 15.84/16.12 (assume @p12 (forall @t5 (= @t12 (forall @t18 (=> @t33 @t16))))) % 15.84/16.12 (assume @p13 @t36) % 15.84/16.12 (assume @p14 (forall @t30 (= (= @t15 @t37) (forall @t29 (= @t28 (and @t32 (not @t31))))))) % 15.84/16.12 (assume @p15 @t39) % 15.84/16.12 (assume @p16 (forall @t5 (= @t7 (and @t12 @t40)))) % 15.84/16.12 (assume @p17 true) % 15.84/16.12 (assume @p18 (tptp.empty tptp.empty_set)) % 15.84/16.12 (assume @p19 (forall @t5 (=> @t42 (not (tptp.empty @t10))))) % 15.84/16.12 (assume @p20 (forall @t5 (=> @t42 (not (tptp.empty @t9))))) % 15.84/16.12 (assume @p21 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 15.84/16.12 (assume @p22 (forall @t5 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 15.84/16.12 (assume @p23 (forall @t5 (not (tptp.proper_subset @t1 @t1)))) % 15.84/16.12 (assume @p24 @t43) % 15.84/16.12 (assume @p25 (forall @t5 (= (tptp.subset @t20 @t2) @t4))) % 15.84/16.12 (assume @p26 (forall @t5 (= (= @t37 tptp.empty_set) @t12))) % 15.84/16.12 (assume @p27 (forall @t30 (=> @t12 (or @t33 (tptp.subset @t1 (tptp.set_difference @t2 (tptp.singleton @t15))))))) % 15.84/16.12 (assume @p28 (forall @t5 (= (tptp.subset @t1 @t44) (or @t24 (= @t1 @t44))))) % 15.84/16.12 (assume @p29 (exists @t25 @t41)) % 15.84/16.12 (assume @p30 (exists @t25 @t42)) % 15.84/16.12 (assume @p31 (forall @t5 (tptp.subset @t1 @t1))) % 15.84/16.12 (assume @p32 (forall @t5 (=> @t38 (tptp.disjoint @t2 @t1)))) % 15.84/16.12 (assume @p33 (forall @t5 (=> @t12 (= @t10 @t2)))) % 15.84/16.12 (assume @p34 (forall @t5 (tptp.subset @t11 @t1))) % 15.84/16.12 (assume @p35 (forall @t30 (=> (and @t12 @t46) (tptp.subset @t1 @t45)))) % 15.84/16.12 (assume @p36 (forall @t25 (= (tptp.set_union2 @t1 tptp.empty_set) @t1))) % 15.84/16.12 (assume @p37 (forall @t30 (=> (and @t12 (tptp.subset @t2 @t15)) @t46))) % 15.84/16.12 (assume @p38 (not @t49)) % 15.84/16.12 (assume @p39 (forall @t30 (=> @t12 (tptp.subset (tptp.set_intersection2 @t1 @t15) @t45)))) % 15.84/16.12 (assume @p40 (forall @t5 (=> @t12 (= @t11 @t1)))) % 15.84/16.12 (assume @p41 (forall @t25 (= (tptp.set_intersection2 @t1 tptp.empty_set) tptp.empty_set))) % 15.84/16.12 (assume @p42 @t52) % 15.84/16.12 (assume @p43 (forall @t25 (tptp.subset tptp.empty_set @t1))) % 15.84/16.12 (assume @p44 (forall @t30 (=> @t12 (tptp.subset (tptp.set_difference @t1 @t15) (tptp.set_difference @t2 @t15))))) % 15.84/16.12 (assume @p45 (forall @t5 (tptp.subset @t37 @t1))) % 15.84/16.12 (assume @p46 (forall @t5 (= @t53 @t10))) % 15.84/16.12 (assume @p47 (forall @t25 (= (tptp.set_difference @t1 tptp.empty_set) @t1))) % 15.84/16.12 (assume @p48 @t63) % 15.84/16.12 (assume @p49 @t65) % 15.84/16.12 (assume @p50 (forall @t5 (= (tptp.set_difference @t10 @t2) @t37))) % 15.84/16.12 (assume @p51 (forall @t5 (=> @t12 (= @t2 @t53)))) % 15.84/16.12 (assume @p52 (forall @t5 (= (tptp.set_difference @t1 @t37) @t11))) % 15.84/16.12 (assume @p53 (forall @t25 (= (tptp.set_difference tptp.empty_set @t1) tptp.empty_set))) % 15.84/16.12 (assume @p54 (forall @t5 (and (not (and @t59 (forall @t18 (not @t66)))) (not (and (exists @t18 @t66) @t38))))) % 15.84/16.12 (assume @p55 (forall @t5 (not (and @t12 @t6)))) % 15.84/16.12 (assume @p56 (forall @t30 (=> (and @t12 (tptp.disjoint @t2 @t15)) (tptp.disjoint @t1 @t15)))) % 15.84/16.12 (assume @p57 (forall @t25 (= (tptp.unordered_pair @t1 @t1) @t20))) % 15.84/16.12 (assume @p58 (forall @t25 (=> @t41 @t24))) % 15.84/16.12 (assume @p59 (forall @t5 (not (and @t4 @t67)))) % 15.84/16.12 (assume @p60 (forall @t5 (tptp.subset @t1 @t10))) % 15.84/16.12 (assume @p61 (forall @t5 (= @t38 (= @t37 @t1)))) % 15.84/16.12 (assume @p62 (forall @t5 (not (and @t41 @t40 @t67)))) % 15.84/16.12 (assume @p63 (forall @t30 (=> (and @t12 (tptp.subset @t15 @t2)) (tptp.subset (tptp.set_union2 @t1 @t15) 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15.84/16.12 (step @p164 :rule trans :premises (@p163 @p154)) % 15.84/16.12 (step @p165 :rule refl :args (@t121)) % 15.84/16.12 (step @p166 :rule nary_cong :premises (@p165 @p164) :args ((and @t121 @t118))) % 15.84/16.12 (step @p167 :rule alpha_equiv :args (@t124 @t125 (@list @t107 @t104))) % 15.84/16.12 (step @p168 :rule alpha_equiv :args (@t128 @t125 (@list @t120 @t119))) % 15.84/16.12 (step @p169 :rule nary_cong :premises (@p168 @p167) :args (@t129)) % 15.84/16.12 (step @p170 :rule quant-miniscope-and :args ((= (forall @t5 (and @t127 @t123)) @t129))) % 15.84/16.12 (step @p171 :rule trans :premises (@p170 @p169)) % 15.84/16.12 (step @p172 :rule trans :premises (@p171 @p166)) % 15.84/16.12 (step @p173 :rule refl :args (@t59)) % 15.84/16.12 (step @p174 :rule bool-double-not-elim :args (@t122)) % 15.84/16.12 (step @p175 :rule nary_cong :premises (@p174 @p173) :args ((or (not @t126) @t59))) % 15.84/16.12 (step @p176 :rule bool-and-de-morgan :args (@t126 @t38 true)) % 15.84/16.12 (step 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:args (@t21)) % 15.84/16.12 (step @p261 :rule cong :premises (@p260 @p259) :args (@t22)) % 15.84/16.12 (step @p262 :rule cong :premises (@p261) :args (@t23)) % 15.84/16.12 (step @p263 :rule eq_resolve :premises (@p7 @p262)) % 15.84/16.12 (step @p264 :rule bool-eq-true :args (@t154)) % 15.84/16.12 (step @p265 :rule eq-symm :args (true @t154)) % 15.84/16.12 (step @p266 :rule trans :premises (@p265 @p264)) % 15.84/16.12 (step @p267 :rule refl :args (@t73)) % 15.84/16.12 (step @p268 :rule eq-symm :args (tptp.empty_set @t15)) % 15.84/16.12 (step @p269 :rule cong :premises (@p268 @p267) :args ((= @t155 @t73))) % 15.84/16.12 (step @p270 :rule eq-symm :args (@t73 @t155)) % 15.84/16.12 (step @p271 :rule trans :premises (@p270 @p269)) % 15.84/16.12 (step @p272 :rule cong :premises (@p271) :args (@t156)) % 15.84/16.12 (step @p273 :rule eq-refl :args (@t47)) % 15.84/16.12 (step @p274 :rule cong :premises (@p273 @p272) :args (@t157)) % 15.84/16.12 (step @p275 :rule trans :premises (@p274 @p266)) % 15.84/16.12 (step @p276 :rule refl :args (@t158)) % 15.84/16.12 (step @p277 :rule cong :premises (@p276 @p275) :args ((=> @t158 @t157))) % 15.84/16.12 (assume-push @p404 @t158) % 15.84/16.12 (step @p279 :rule instantiate :premises (@p263) :args (@t77)) % 15.84/16.12 (step-pop @p405 :rule scope :premises (@p279)) % 15.84/16.12 (step @p280 :rule process_scope :premises (@p405) :args (@t157)) % 15.84/16.12 (step @p282 :rule eq_resolve :premises (@p280 @p277)) % 15.84/16.12 (step @p283 :rule implies_elim :premises (@p282)) % 15.84/16.12 (step @p284 :rule chain_m_resolution :premises (@p283 @p263) :args (@t154 @t72 (@list @t158))) % 15.84/16.12 (step @p285 :rule eq-symm :args (@t132 tptp.empty_set)) % 15.84/16.12 (step @p286 :rule refl :args (@t151)) % 15.84/16.12 (step @p287 :rule cong :premises (@p286 @p285) :args ((= @t151 @t159))) % 15.84/16.12 (step @p288 :rule eq-symm :args (@t159 @t151)) % 15.84/16.12 (step @p289 :rule trans :premises (@p288 @p287)) % 15.84/16.12 (step @p290 :rule refl :args (@t154)) % 15.84/16.12 (step @p291 :rule cong :premises (@p290 @p289) :args ((=> @t154 @t160))) % 15.84/16.12 (assume-push @p406 @t154) % 15.84/16.12 (step @p293 :rule instantiate :premises (@p284) :args ((@list @t132))) % 15.84/16.12 (step-pop @p407 :rule scope :premises (@p293)) % 15.84/16.12 (step @p294 :rule process_scope :premises (@p407) :args (@t160)) % 15.84/16.12 (step @p296 :rule eq_resolve :premises (@p294 @p291)) % 15.84/16.12 (step @p297 :rule implies_elim :premises (@p296)) % 15.84/16.12 (step @p298 :rule chain_m_resolution :premises (@p297 @p284) :args (@t162 @t72 @t163)) % 15.84/16.12 (step @p299 :rule cnf_equiv_pos1 :args (@t162)) % 15.84/16.12 (step @p300 :rule reordering :premises (@p299) :args ((or @t164 @t161 (not @t162)))) % 15.84/16.12 (step @p301 :rule chain_m_resolution :premises (@p300 @p255 @p298) :args (@t161 @t146 (@list @t151 @t162))) % 15.84/16.12 (step @p302 :rule refl :args (@t165)) % 15.84/16.12 (step @p303 :rule bool-double-not-elim :args (@t83)) % 15.84/16.12 (step @p304 :rule refl :args (@t166)) % 15.84/16.12 (step @p305 :rule refl :args (@t164)) % 15.84/16.12 (step @p306 :rule nary_cong :premises (@p305 @p304 @p303 @p302) :args ((or @t164 @t166 (not @t167) @t165))) % 15.84/16.12 (assume-push @p408 @t151) % 15.84/16.12 (assume-push @p409 @t161) % 15.84/16.12 (assume-push @p410 @t91) % 15.84/16.12 (assume-push @p411 @t167) % 15.84/16.12 (step @p311 :rule evaluate :args (@t168)) % 15.84/16.12 (step @p312 :rule true_intro :premises (@p255)) % 15.84/16.12 (step @p313 :rule refl :args (@t47)) % 15.84/16.12 (step @p314 :rule symm :premises (@p410)) % 15.84/16.12 (step @p315 :rule trans :premises (@p314 @p301)) % 15.84/16.12 (step @p316 :rule cong :premises (@p315 @p313) :args (@t83)) % 15.84/16.12 (step @p317 :rule false_intro :premises (@p411)) % 15.84/16.12 (step @p318 :rule symm :premises (@p317)) % 15.84/16.12 (step @p319 :rule trans :premises (@p318 @p316 @p312)) % 15.84/16.12 (step @p320 false :rule eq_resolve :premises (@p319 @p311)) % 15.84/16.12 (step-pop @p412 :rule scope :premises (@p320)) % 15.84/16.12 (step-pop @p413 :rule scope :premises (@p412)) % 15.84/16.12 (step-pop @p414 :rule scope :premises (@p413)) % 15.84/16.12 (step-pop @p415 :rule scope :premises (@p414)) % 15.84/16.12 (step @p321 :rule process_scope :premises (@p415) :args (false)) % 15.84/16.12 (assume-push @p416 @t151) % 15.84/16.12 (assume-push @p417 @t161) % 15.84/16.12 (assume-push @p418 @t167) % 15.84/16.12 (assume-push @p419 @t91) % 15.84/16.12 (step @p330 :rule and_intro :premises (@p255 @p301 @p419 @p418)) % 15.84/16.12 (step-pop @p420 :rule scope :premises (@p330)) % 15.84/16.12 (step-pop @p421 :rule scope :premises (@p420)) % 15.84/16.12 (step-pop @p422 :rule scope :premises (@p421)) % 15.84/16.12 (step-pop @p423 :rule scope :premises (@p422)) % 15.84/16.12 (step @p331 :rule process_scope :premises (@p423) :args (@t169)) % 15.84/16.12 (step @p336 :rule implies_elim :premises (@p331)) % 15.84/16.12 (step @p337 :rule resolution :premises (@p336 @p321) :args (true @t169)) % 15.84/16.12 (step @p338 :rule not_and :premises (@p337)) % 15.84/16.12 (step @p339 :rule eq_resolve :premises (@p338 @p306)) % 15.84/16.12 (step @p340 :rule chain_m_resolution :premises (@p339 @p301 @p255 @p114 @p112 @p97 @p96) :args (@t86 (@list false false false false true true) (@list @t161 @t151 @t91 @t92 @t83 @t85))) % 15.84/16.12 (step @p341 :rule refl :args (@t83)) % 15.84/16.12 (step @p342 :rule cong :premises (@p341 @p101) :args ((= @t83 @t87))) % 15.84/16.12 (step @p343 :rule eq-symm :args (@t87 @t83)) % 15.84/16.12 (step @p344 :rule trans :premises (@p343 @p342)) % 15.84/16.12 (step @p345 :rule cong :premises (@p290 @p344) :args ((=> @t154 @t170))) % 15.84/16.12 (assume-push @p424 @t154) % 15.84/16.12 (step @p347 :rule instantiate :premises (@p284) :args (@t90)) % 15.84/16.12 (step-pop @p425 :rule scope :premises (@p347)) % 15.84/16.12 (step @p348 :rule process_scope :premises (@p425) :args (@t170)) % 15.84/16.12 (step @p350 :rule eq_resolve :premises (@p348 @p345)) % 15.84/16.12 (step @p351 :rule implies_elim :premises (@p350)) % 15.84/16.12 (step @p352 :rule chain_m_resolution :premises (@p351 @p284) :args (@t171 @t72 @t163)) % 15.84/16.12 (step @p353 :rule cnf_equiv_neg1 :args (@t85)) % 15.84/16.12 (step @p354 :rule reordering :premises (@p353) :args ((or @t84 @t83 @t85))) % 15.84/16.12 (step @p355 :rule chain_m_resolution :premises (@p354 @p340 @p96) :args (@t83 @t153 (@list @t84 @t85))) % 15.84/16.12 (step @p356 :rule cnf_equiv_pos1 :args (@t171)) % 15.84/16.12 (step @p357 :rule reordering :premises (@p356) :args ((or @t167 @t91 (not @t171)))) % 15.84/16.12 (step @p358 :rule chain_m_resolution :premises (@p357 @p355 @p352) :args (@t91 @t146 (@list @t83 @t171))) % 15.84/16.12 (step @p359 :rule bool-double-not-elim :args (@t84)) % 15.84/16.12 (step @p360 :rule refl :args (@t172)) % 15.84/16.12 (step @p361 :rule nary_cong :premises (@p360 @p359 @p302) :args ((or @t172 (not @t86) @t165))) % 15.84/16.12 (assume-push @p426 @t68) % 15.84/16.12 (assume-push @p427 @t91) % 15.84/16.12 (assume-push @p428 @t86) % 15.84/16.12 (step @p311 :rule evaluate :args (@t168)) % 15.84/16.12 (step @p365 :rule true_intro :premises (@p79)) % 15.84/16.12 (step @p366 :rule refl :args (tptp.empty_set)) % 15.84/16.12 (step @p367 :rule symm :premises (@p427)) % 15.84/16.12 (step @p368 :rule cong :premises (@p367 @p366) :args (@t84)) % 15.84/16.12 (step @p369 :rule false_intro :premises (@p428)) % 15.84/16.12 (step @p370 :rule symm :premises (@p369)) % 15.84/16.12 (step @p371 :rule trans :premises (@p370 @p368 @p365)) % 15.84/16.12 (step @p372 false :rule eq_resolve :premises (@p371 @p311)) % 15.84/16.12 (step-pop @p429 :rule scope :premises (@p372)) % 15.84/16.12 (step-pop @p430 :rule scope :premises (@p429)) % 15.84/16.12 (step-pop @p431 :rule scope :premises (@p430)) % 15.84/16.12 (step @p373 :rule process_scope :premises (@p431) :args (false)) % 15.84/16.12 (assume-push @p432 @t68) % 15.84/16.12 (assume-push @p433 @t86) % 15.84/16.12 (assume-push @p434 @t91) % 15.84/16.12 (step @p380 :rule and_intro :premises (@p79 @p434 @p433)) % 15.84/16.12 (step-pop @p435 :rule scope :premises (@p380)) % 15.84/16.12 (step-pop @p436 :rule scope :premises (@p435)) % 15.84/16.12 (step-pop @p437 :rule scope :premises (@p436)) % 15.84/16.12 (step @p381 :rule process_scope :premises (@p437) :args (@t173)) % 15.84/16.12 (step @p385 :rule implies_elim :premises (@p381)) % 15.84/16.12 (step @p386 :rule resolution :premises (@p385 @p373) :args (true @t173)) % 15.84/16.12 (step @p387 :rule not_and :premises (@p386)) % 15.84/16.12 (step @p388 :rule eq_resolve :premises (@p387 @p361)) % 15.84/16.12 (step @p389 false :rule chain_m_resolution :premises (@p388 @p358 @p340 @p79) :args (false (@list false true false) (@list @t91 @t84 @t68))) % 15.84/16.12 ) % 15.84/16.12 % SZS output end Proof % 15.84/16.12 % cvc5 exiting %------------------------------------------------------------------------------